A fast approximate kernel k-means clustering method for large data sets

Abstract

In unsupervised classification, kernel k-means clustering method has been shown to perform better than conventional k-means clustering method in identifying non-isotropic clusters in a data set. The space and time requirements of this method are O(n2), where n is the data set size. The paper proposes a two stage hybrid approach to speed-up the kernel k-means clustering method. In the first stage, the data set is divided in to a number of group-lets by employing a fast clustering method called leaders clustering method. Each group-let is represented by a prototype called its leader. The set of leaders, which depends on a threshold parameter, can be derived in O(n) time. The paper presents a modification to the leaders clustering method where group-lets are found in the kernel space (not in the input space), but are represented by leaders in the input space. In the second stage, kernel k-means clustering method is applied with the set of leaders to derive a partition of the set of leaders. Finally, each leader is replaced by its group to get a partition of the data set. The proposed method has time complexity of O(n+p2), where p is the leaders set size. Its space complexity is also O(n+p2). The proposed method can be easily implemented. Experimental results shows that, with a small loss of quality, the proposed method can significantly reduce the time taken than the conventional kernel k-means clustering method.